An automated height transformation using precise geoid models

Abstract

In most of the countries, national height systems are referenced to the mean sea level (geoid) whereas using GPS technique in positioning provides ellipsoidal heights. However, these GPS ellipsoidal heights h can be transformed into the orthometric heights from the geoid H depending on a simple relation among the heights, and this transformation requires to know the geoid undulations N ( H = h - N ). The methods for deriving the geoid undulation at a point are various and practicality of the method is one of the major concerns as well as its precision. In this study, an experiment on calculating local geoids using an algorithm based on surface polynomials with weighted corrections was performed and a program, which computes the geoid undulation at a point in the local area using the model was developed, and an executable file of the program was inserted into the commercial GPS data processing software as “height transformation module”. With this ad hoc module, the software provides the orthometric heights to the user at the same time with the three dimensional geodetic coordinates of the points. Hence, an automated height transformation, without user intervention, simultaneously with GPS data post-processes is provided. The experiment data includes dense and well distributed 301 GPS/levelling benchmarks in the west of Turkey. All the decisions regarding the data preparation and modelling process using polynomials (such as detecting the blunders in the data, determining the optimal degree of the polynomial and testing significance of the polynomial coefficients etc.) are critical in practice and were dealt in the study as well. The orthometric heights of the test benchmarks were provided with 3.5 cm accuracy by the automated height transformation module.